Question: Michael is 3 times as old as William. Twelve years ago, Michael was 9 times as old as William. How old is Michael now?
Solution: We can use the given information to write down two equations that describe the ages of Michael and William. Let Michael's current age be $m$ and William's current age be $w$ The information in the first sentence can be expressed in the following equation: $m = 3w$ Twelve years ago, Michael was $m - 12$ years old, and William was $w - 12$ years old. The information in the second sentence can be expressed in the following equation: $m - 12 = 9(w - 12)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $m$ , it might be easiest to solve our first equation for $w$ and substitute it into our second equation. Solving our first equation for $w$ , we get: $w = m / 3$ . Substituting this into our second equation, we get: $m - 12 = 9($ $(m / 3)$ $- 12)$ which combines the information about $m$ from both of our original equations. Simplifying the right side of this equation, we get: $m - 12 = 3 m - 108$ Solving for $m$ , we get: $2 m = 96$ $m = \dfrac{1}{2} \cdot 96 = 48$.